Q101 / 197 · NEET 2009 (Mains) · Physics
An explosion blows a rock into three parts Two parts go off at right angles to each other. These two are, $1 \mathrm{~kg}$ first part moving with a velocity of $12 \mathrm{~ms}^{-1}$ and $2 \mathrm{~kg}$ second part moving with a velocity of $8 \mathrm{~ms}^{-1}$. If the thirds part files off with a velocity of $4 \mathrm{~ms}^{-1}$, its mass would be :
- A$3 \mathrm{~kg}$
- Correct answerB$5 \mathrm{~kg}$
- C$7 \mathrm{~kg}$
- D$17 \mathrm{~kg}$
Solution
$$
\begin{aligned}
\overrightarrow{\mathrm{P}}_1+\overrightarrow{\mathrm{P}}_2+\overrightarrow{\mathrm{P}}_3 & =0 \\
\left|\overrightarrow{\mathrm{P}}_3\right| & =\left|\overrightarrow{\mathrm{P}}_1+\overrightarrow{\mathrm{P}}_2\right| \\
\mathrm{m} \times 4 & =\sqrt{\mathrm{P}_1^2+\mathrm{P}_2^2} \\
& =\sqrt{12^2+16^2} \\
\mathrm{~m} & =5 \mathrm{~kg}
\end{aligned}
$$
Hence, the correct answer is option: 'B'.